A Physics Informed Neural Network Approach to Solution and Identification of Biharmonic Equations of Elasticity
This addresses a specific problem in computational mechanics for researchers and engineers, but it is incremental as it extends PINNs to a new type of PDE without broader methodological breakthroughs.
The paper tackled solving biharmonic equations in elasticity, which are challenging fourth-order PDEs, by applying Physics Informed Neural Networks (PINNs) with Airy stress functions and Fourier series, resulting in accurate and fast solutions with minimal parameters.
We explore an application of the Physics Informed Neural Networks (PINNs) in conjunction with Airy stress functions and Fourier series to find optimal solutions to a few reference biharmonic problems of elasticity and elastic plate theory. Biharmonic relations are fourth-order partial differential equations (PDEs) that are challenging to solve using classical numerical methods, and have not been addressed using PINNs. Our work highlights a novel application of classical analytical methods to guide the construction of efficient neural networks with the minimal number of parameters that are very accurate and fast to evaluate. In particular, we find that enriching feature space using Airy stress functions can significantly improve the accuracy of PINN solutions for biharmonic PDEs.